AFM: Unit 6 Exponentials & Logarithms Review

Exponential Functions & Equations

100

What is the y-intercept of the function:

y=2(3/2)^x

2

200

What is the asymptote of the function:

y = 2(3/2)^x 

y=0

300

Which is true about the function y=e^x ?

I. It represents exponential growth.

II. It represents exponential decay.

III. It passes through (0,1)

IV. It passes through (1,0)

I and III only

400

To shift the graph of y=3^x two units to the right, what is the new equation?

y=3^x-2

500

Solve:

3(27)^x = 1

x= 1/9

Exponential Applications

100

A magazine had 4000 subscribers at the end of the year 2004. The number of subscribers increased by 10% each year as compared with the previous year.

How many subscribers are there at the end of the year 2007 ?

5324

200

James purchased a truck for $25,900. The value of the truck decreases by 12% per year. What will be the approximate value 8 years after the purchase?

$9,314.53

300

When interest is compounded n times a year, the accumulated amount (A) after t years is given by the formula:

A = P(1 + ^r/_n)^nt

where P is the initial principal and r is the annual rate of interest. Approximately how long, to the nearest hundredth, will it take $2,000 to double at an annual interest rate of 5.25% compounded monthly?

13.23 years

400

Drew's parents invested $1,500 in an account such that the value of the investment doubles every seven years. The value of the investment, V, is determined by the equation V = 1500(2)^t/7, where t represents the number of years since the money was deposited. How many years, to the nearest tenth of a year, will it take the value of the investment to reach $1,000,000?

65.7 years

500

The Wongs bought a new house three years ago for $92,000. The house is now worth about $113,000. Assuming a steady annual percentage growth rate, approximately what was the yearly rate of appreciation?

7.1%

Log Laws

100

Expand 

log(4x)

log(4) + log(x)

200

If x= r²/s, write an equivalent expression to log(x). (Expand.)

2log(r) - log(s)

300

Which expression is not equivalent to log_b(36)?

A.  6log_b(2)

B.  log_b(9) + log_b(4)

C.  2log_b(6)

D.  log_b(72) - log_b(2)

A.  6log_b(2)

400

If  ln(M) = 3ln(r) + 2ln(s), then express M in terms of r and s.

r³s²

500

If log5=a, then express log250 in terms of a.

2a + 1

Log Equations

100

If log₄x = 3, then what is x?

64

200

What is the solution to the equation:

log₂(8) + log₂(32) = x

8

300

If log(x) = 2 + log(2), then what is x?

200

400

If log(N) = 2log(x) + log(y), what is N in terms of x and y?

x²y

500

Solve:

log₅(2x+1) + log₅(x) = log₅(10)

2

Solving with Logs

100

5^3x-2 = 25

4/3

200

Which of the following statements is/are true based on the definition of a logarithm y = log_b(x)?

I.  x > 0

II.  b > 0

III.  b not equal to 1

IV.  y > 0

I, II, and III only

300

Given a starting population of 100 bacteria, the formula b = 100(2^t) can be used to find the number of bacteria, b, after t periods of time. If each period is 15 minutes long, how many minutes will it take for the population of bacteria to reach 51,200?

135 minutes

400

Kristen invests $5,000 in a bank. The bank pays 6% interest compounded monthly. To the nearest tenth of a year, how long must she leave the money in the bank for it to double? 

11.6 years

500

The number of bacteria present in a Petri dish can be modeled by the function N = 50e^3t, where N is the number of bacteria present in the Petri dish after t hours. Using this model, determine, to the nearest hundredth, the number of hours it will take for N to reach 30,700.

2.14 hours